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Microscopic structural response of nanoparticles in styrene–butadiene rubber under cyclic uniaxial elongation


Changes in the aggregated structure of silica in styrene–butadiene rubber are measured with small-angle X-ray scattering under cyclic uniaxial elongation. We employ a spherical harmonics expansion approach to quantitatively analyze the anisotropic scattering data and to separate the anisotropic response of the silica’s configuration upon the elongation from the isotropic component. The results clearly show inhomogeneity in microscopic deformation upon elongation. Phase lag between microscopic structural responses and macroscopic strain are also observed. This study demonstrates that the combination of time-resolved small-angle scattering measurement and an analysis using spherical harmonics expansion is quite useful for exploring the structural response of filled rubber systems to an external deformation.

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  1. 1.

    Koga T, Hashimoto T, Takenaka M, Aizawa K, Amino N, Nakamura M, et al. New insight into hierarchical structures of carbon black dispersed in polymer matrices: a combined small-angle scattering study. Macromolecules. 2008;41:453–64.

    CAS  Article  Google Scholar 

  2. 2.

    Koga T, Takenaka M, Aizawa K, Nakamura M, Hashimoto T. Structure factors of dispersible units of carbon black filler in rubbers. Langmuir. 2005;21:11409–13.

    CAS  Article  Google Scholar 

  3. 3.

    Hyeon-Lee J, Beaucage G, Pratsinis S, Vemury S. Fractal analysis of flame-synthesized nanostructured silica and titania powders using small-angle X-ray scattering. Langmuir. 1998;14:5751–6.

    CAS  Article  Google Scholar 

  4. 4.

    Schaefer D, Rieker T, Agamalian M, Lin J, Fischer D, Sukumaran S, et al. Multilevel structure of reinforcing silica and carbon. J Appl Cryst. 2000;33:587–91.

    CAS  Article  Google Scholar 

  5. 5.

    Kammler HK, Beaucage G, Mueller R, Pratsinis SE. Structure of flame-made silica nanoparticles by ultra-small-angle X-ray scattering. Langmuir. 2004;20:1915–21.

    CAS  Article  Google Scholar 

  6. 6.

    Baeza GP, Genix A-C, Degrandcourt C, Petitjean L, Gummel J, Oberdisse J. Multiscale filler structure in simplified industrial nanocomposite silica/SBR systems studied by SAXS and TEM. Macromolecules. 2012;46:317–29.

    Article  Google Scholar 

  7. 7.

    Kishimoto H, Shinohara Y, Amemiya Y, Inoue K, Suzuki Y, Takeuchi A, et al. Structural analysis of filler in rubber composite under stretch with time-resolved two-dimensional ultra-small-angle X-ray scattering. Rubber Chem Tech. 2008;81:541–51.

    CAS  Article  Google Scholar 

  8. 8.

    Genix A-C, Oberdisse J. Structure and dynamics of polymer nanocomposites studied by X-ray and neutron scattering techniques. Curr Opin Colloid Interface. 2015;20:293–303.

    CAS  Article  Google Scholar 

  9. 9.

    Ehrburger-Dolle F, Bley F, Geissler E, Livet F, Morfin I, Rochas C. Filler networks in elastomers. Macromol Symp. 2003;200:157–67.

    CAS  Article  Google Scholar 

  10. 10.

    Ehrburger-Dolle F, Hindermann-Bischoff M, Livet F, Bley F, Rochas C, Geissler E. Anisotropic ultra-small-angle X-ray scattering in carbon black filled polymers. Langmuir. 2001;17:329–34.

    CAS  Article  Google Scholar 

  11. 11.

    Mendes J Jr., Lindner P, Buzier M, Boué F, Bastide J. Experimental evidence for inhomogeneous swelling and deformation in statistical gels. Phys Rev Lett. 1991;66:1595–8.

    CAS  Article  Google Scholar 

  12. 12.

    Bastide J, Leibler L, Prost J. Scattering by deformed swollen gels—butterfly isointensity patterns. Macromolecules. 1990;23:1821–5.

    CAS  Article  Google Scholar 

  13. 13.

    Koizumi S, Monkenbusch M, Richter D, Schwahn D, Farago B. Concentration fluctuations in polymer gel investigated by neutron scattering: Static inhomogeneity in swollen gel. J Chem Phys. 2004;121:12721–31.

    CAS  Article  Google Scholar 

  14. 14.

    Oberdisse J. Aggregation of colloidal nanoparticles in polymer matrices. Soft Matter. 2006;2:29–36.

    CAS  Article  Google Scholar 

  15. 15.

    Pyckhout-Hintzen W, Urban V, Belina G, Straube E, Kluppel M, Heinrich G. Microscopic deformation of filler particles in rubber under uniaxial deformation. Macromol Symp. 2003;200:121–8.

    Article  Google Scholar 

  16. 16.

    Nishi K, Shibayama M. 2D pair distribution function analysis of anisotropic small-angle scattering patterns from elongated nano-composite hydrogels. Soft Matter. 2017;13:3076–83.

    CAS  Article  Google Scholar 

  17. 17.

    Kishimoto H, Shinohara Y, Suzuki Y, Takeuchi A, Yagi N, Amemiya Y. Pinhole-type two-dimensional ultra-small-angle X-ray scattering on the micrometer scale. J Synchrotron Rad. 2014;21:1–4.

    Article  Google Scholar 

  18. 18.

    Wang Z, Lam CN, Chen W-R, Wang W, Liu J, Liu Y, et al. Fingerprinting molecular relaxation in deformed polymers. Phys Rev X. 2017;7:179–17.

    Google Scholar 

  19. 19.

    Huang G-R, Bin W, Wang Y, Chen W-R. Characterization of microscopic deformation through two-point spatial correlation functions. Phys Rev E. 2018;97:012605.

    CAS  Article  Google Scholar 

  20. 20.

    Suzuki Y, Haimovich J, Egami T. Bond-orientational anisotropy in metallic glasses observed by x-ray diffraction. Phys Rev B. 1987;35:2162–8.

    CAS  Article  Google Scholar 

  21. 21.

    Hess S. Shear-flow-induced distortion of the pair-correlation function. Phys Rev A. 1980;22:2844–8.

    CAS  Article  Google Scholar 

  22. 22.

    Dmowski W, Iwashita T, Chuang CP, Almer J, Egami T. Elastic heterogeneity in metallic glasses. Phys Rev Lett. 2010;105:205502.

    CAS  Article  Google Scholar 

  23. 23.

    Wagner NJ, Ackerson BJ. Analysis of nonequilibrium structures of shearing colloidal suspensions. J Chem Phys. 1992;97:1473–83.

    CAS  Article  Google Scholar 

  24. 24.

    Livet F, Bley F, Ehrburger-Dolle F, Morfin I, Geissler E, Sutton M. X-ray intensity fluctuation spectroscopy by heterodyne detection. J Synchrotron Rad. 2006;13:453–8.

    CAS  Article  Google Scholar 

  25. 25.

    Ehrburger-Dolle F, Morfin I, Bley F, Livet F, Heinrich G, Richter S, et al. XPCS investigation of the dynamics of filler particles in stretched filled elastomers. Macromolecules. 2012;45:8691–701.

    CAS  Article  Google Scholar 

  26. 26.

    Kraft P, Bergamaschi A, Broennimann C, Dinapoli R, Eikenberry EF, Henrich B, et al. Performance of single-photon-counting PILATUS detector modules. J Synchrotron Rad. 2009;16:368–75.

    CAS  Article  Google Scholar 

  27. 27.

    Masunaga H, Ogawa H, Takano T, Sasaki S, Goto S, Tanaka T, et al. Multipurpose soft-material SAXS/WAXS/GISAXS beamline at SPring-8. Polym J. 2011;43:471–7.

    CAS  Article  Google Scholar 

  28. 28.

    Shinohara Y, Imai R, Kishimoto H, Yagi N, Amemiya Y. Indirectly illuminated X-ray area detector for X-ray photon correlation spectroscopy. J Synchrotron Rad. 2010;17:737–42.

    CAS  Article  Google Scholar 

  29. 29.

    Shinohara Y, Kishimoto H, Yagi N, Amemiya Y. Microscopic observation of aging of silica particles in unvulcanized rubber. Macromolecules. 2010;43:9480–7.

    CAS  Article  Google Scholar 

  30. 30.

    Shinohara Y, Amemiya Y. Effect of finite spatial coherence length on small-angle scattering. J Appl Cryst. 2015;48:1660–4.

    CAS  Article  Google Scholar 

  31. 31.

    Wang Z, Iwashita T, Porcar L, Wang Y, Liu Y, Sanchez-Diaz LE, et al. Local elasticity and dynamical heterogeneity in nonlinear rheology of interacting colloidal glasses revealed by neutron scattering and rheometry. arXiv. 2016;1611:03135.

    Google Scholar 

  32. 32.

    Livet F, Abernathy DL, Bley F, Caudron R, Geissler E, Detlefs C, et al. Kinetic evolution of unmixing in an AlLi alloy using X-ray intensity fluctuation spectroscopy. Phys Rev E. 2001;63:036108.

    CAS  Article  Google Scholar 

  33. 33.

    Sutton M, Laaziri K, Livet F, Bley F. Using coherence to measure two-time correlation functions. Opt Express. 2003;11:2268–77.

    CAS  Article  Google Scholar 

  34. 34.

    Evenson Z, Ruta B, Hechler S, Stolpe M, Pineda E, Gallino I, et al. X-ray photon correlation spectroscopy reveals intermittent aging dynamics in a metallic glass. Phys Rev Lett. 2015;115:175701.

    Article  Google Scholar 

  35. 35.

    Conrad H, Lemkühler F, Fischer B, Westermeier F, Schroer MA, Chushkin Y, et al. Correlated heterogeneous dynamics in glass-forming polymers. Phys Rev E. 2015;91:042309.

    CAS  Article  Google Scholar 

  36. 36.

    Madsen A, Leheny RL, Guo H, Sprung M, Czakkel O. Beyond simple exponential correlation functions and equilibrium dynamics in X-ray photon correlation spectroscopy. New J Phys. 2010;12:055001.

    Article  Google Scholar 

  37. 37.

    Rogers MC, Chen K, Andrzejewski L, Narayanan S, Ramakrishnan S, Leheny RL, et al. Echoes in X-ray speckles track nanometer-scale plastic events in colloidal gels under shear. Phys Rev E. 2014;90:062310.

    Article  Google Scholar 

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We thank Hiroyasu Masunaga (JASRI/SPring-8) for his support at BL03XU. The SAXS and XPCS measurements were supported by Chikara Sasaki and Daiki Kikutake (University of Tokyo) and were conducted under the approval of SPring-8 Proposal Review Committee (Proposal No. 2014A1287, 2014A7209, 2014B1490, 2014B7259, 2015A1625, 2015A7209, 2015B1425, 2015B7259, 2016A1368, 2016A7209, 2016B1512, 2016B7209). Preliminary measurements of XPCS were conducted at BL40XU, SPring-8 (Proposal No. 2014B1069). This study was partially supported by “Photon and Quantum Basic Research Coordinated Development Program” from the Ministry of Education, Culture, Sports, Science and Technology, Japan. Y.S. is thankful for the discussion with Wei-Ren Chen (ORNL).  The authors declare no competing financial interests.

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Correspondence to Yuya Shinohara.

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Shinohara, Y., Kishimoto, H., Masui, T. et al. Microscopic structural response of nanoparticles in styrene–butadiene rubber under cyclic uniaxial elongation. Polym J 51, 161–171 (2019).

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